Related papers: General Refraction Problems with Phase Discontinui…
Metasurfaces are ultra-thin optical elements composed of engineered sub-wavelength structures that enable precise control of light. Their inverse design - determining a geometry that yields a desired optical response - is challenging due to…
Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing…
The propagation and refraction of waves in dispersive media are considered. A primary objective is to determine whether waves refract as monochromatic waves by Snell's law with phase velocity or as wave packets. The refraction of wave…
In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these…
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing…
Deflectometry as a technical approach to assessing reflective surfaces has now existed for almost 40 years. Different aspects and variations of the method have been studied in multiple theses and research articles, and reviews are also…
Diffraction of a surface wave on a rectangular wedge with impedance faces is studied using the Sommerfeld-Malyuzhinets technique. An analog of Landau's bypass rule in the theory of plasma waves is introduced for selection of a correct…
We examine the onset of superfluid instabilities for geometries that exhibit hyperscaling violation and Lifshitz-like scaling at infrared and intermediate energy scales, and approach AdS in the ultraviolet. In particular, we are interested…
In this paper we shall initiate the study of the two- and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of…
Conventional phased-array metasurfaces utilize resonant nanoparticles or nanowaveguides to specify spatially-dependent amplitude and phase responses to light. In nearly all these implementations, subwavelength-scale elements are stitched…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
Metasurfaces are subwavelength structured thin films consisting of arrays of units that allow the controls of polarization, phase and amplitude of light over a subwavelength thickness. The recent developments in topological photonics have…
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…
Waveguides are critically important components in microwave, THz, and optical technologies. Due to recent progress in two-dimensional materials, metasurfaces can be efficiently used to design novel waveguide structures which confine the…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
A general framework is developed to study the deformation and stress response in F{\"o}ppl-von K{\'a}rm{\'a}n shallow shells for a given distribution of defects, such as dislocations, disclinations, and interstitials, and metric anomalies,…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We investigate the universal property of curvatures in surface models which display a flat phase and a rough phase whose criticality is described by the Gaussian model. Earlier we derived a relation between the Hessian of the free energy…
Inhomogeneous metasurfaces have shown possibilities for unprecedented control of wave propagation and scattering. While it is conventional to shine a single incident plane wave from one side of these metastructures, illuminating by several…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…